Problem: Solve for $x$ : $4x^2 - 4x - 120 = 0$
Explanation: Dividing both sides by $4$ gives: $ x^2 {-1}x {-30} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-30$ , so we need to find two numbers that add up to $-1$ and multiply to $-30$ The two numbers $5$ and $-6$ satisfy both conditions: $ {5} + {-6} = {-1} $ $ {5} \times {-6} = {-30} $ $(x + {5}) (x {-6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x -6) = 0$ $x + 5 = 0$ or $x - 6 = 0$ Thus, $x = -5$ and $x = 6$ are the solutions.